Final answer:
There are 18 ways to make change for 85 cents using only nickels and/or dimes.
Step-by-step explanation:
To find the number of ways to make change for 85 cents using only nickels and/or dimes, we can use a combination of exhaustive listing and reasoning. We can start by considering all the possible combinations of nickels and dimes that add up to 85 cents.
Let's start with using zero nickels. In this case, we need to use 8 dimes to make 80 cents. So, there is only 1 way to make change with zero nickels.
Next, let's consider using one nickel. Now, we need to use 7 dimes to make 80 cents, since the nickel accounts for 5 cents. Again, there is only 1 way to make change with one nickel.
We can continue this process, increasing the number of nickels used and decreasing the number of dimes, until we reach the maximum number of nickels that can be used (17). At each step, we subtract the value of the nickels from 85 cents and calculate how many dimes are needed to make up the remaining value.
By adding up all the possible combinations, we find that there are a total of 18 ways to make change for 85 cents using only nickels and/or dimes.